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THE RQR algorithm

arXiv 2024年

作者： Camps, Daan Mach, Thomas Vandebril, Raf Watkins, David S. National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory United States University of Potsdam Institute of Mathematics Karl-Liebknecht-Str. 24–25 Potsdam14476 Germany Department of Computer Science KU Leuven Belgium Department of Mathematics Washington State University United States

Pole-swapping algorithms, generalizations of bulge-chasing algorithms, have been shown to be a viable alternative to the bulge-chasing QZ algorithm for solving the generalized eigenvalue problem for a matrix pencil A − λB. It is natural to try to devise a pole-swapping algorithm that solves the standard eigenvalue problem for a single matrix A. This paper introduces such an algorithm and shows that it is competitive with Francis’s bulge-chasing QR *** Codes 65F15, 15A18 © 2024, CC BY.

关键词： consensus algorithm

SPINEX_ Symbolic Regression: Similarity-based Symbolic Regression with Explainable Neighbors Exploration

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arXiv 2024年

作者： Naser, M.Z. Naser, Ahmed Z. Clemson University United States Clemson University United States Department of Mechanical Engineering University of Manitoba Canada

This article introduces a new symbolic regression algorithm based on the SPINEX (Similarity-based Predictions with Explainable Neighbors Exploration) family. This new algorithm (SPINEX_SymbolicRegression) adopts a similarity-based approach to identifying high-merit expressions that satisfy accuracy- and structural similarity metrics. We conducted extensive benchmarking tests comparing SPINEX_SymbolicRegression to over 180 mathematical benchmarking functions from international problem sets that span randomly generated expressions and those based on real physical phenomena. Then, we evaluated the performance of the proposed algorithm in terms of accuracy, expression similarity in terms of presence operators and variables (as compared to the actual expressions), population size, and number of generations at convergence. The results indicate that SPINEX_SymbolicRegression consistently performs well and can, in some instances, outperform leading algorithms. In addition, the algorithm's explainability capabilities are highlighted through in-depth experiments. © 2024, CC BY.

关键词： consensus algorithm

UTILITARIAN algorithm CONFIGURATION FOR INFINITE PARAMETER SPACES

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arXiv 2024年

作者： Graham, Devon R. Leyton-Brown, Kevin Department of Computer Science University of British Columbia VancouverBC Canada

Utilitarian algorithm configuration is a general-purpose technique for automatically searching the parameter space of a given algorithm to optimize its performance, as measured by a given utility function, on a given set of inputs. Recently introduced utilitarian configuration procedures offer optimality guarantees about the returned parameterization while provably adapting to the hardness of the underlying problem. However, the applicability of these approaches is severely limited by the fact that they only search a finite, relatively small set of parameters. They cannot effectively search the configuration space of algorithms with continuous or uncountable parameters. In this paper we introduce a new procedure, which we dub COUP (Continuous, Optimistic Utilitarian Procrastination). COUP is designed to search infinite parameter spaces efficiently to find good configurations quickly. Furthermore, COUP maintains the theoretical benefits of previous utilitarian configuration procedures when applied to finite parameter spaces but is significantly faster, both provably and experimentally. © 2024, CC BY.

关键词： consensus algorithm

A memory and gate efficient algorithm for unitary mixed Schur sampling

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arXiv 2024年

作者： Cervero-Martín, Enrique Mančinska, Laura Theil, Elias Centre for Quantum Technologies National University of Singapore Singapore Centre for the Mathematics of Quantum Theory University of Copenhagen Denmark

We formalize the task of unitary Schur sampling —an extension of weak Schur sampling—which is the process of measuring the Young label and the unitary group register of an input m qudit state. Intuitively, this task is equivalent to applying the Schur transform, projecting onto the isotypic subspaces of the unitary and symmetric groups indexed by the Young labels, and discarding of the permutation register. As such unitary Schur sampling is the natural task in processes such as quantum state tomography or spectrum estimation. We generalize this task to unitary mixed Schur sampling to account for the recently introduced mixed Schur-Weyl transform. We provide a streaming algorithm which achieves an exponential reduction in the memory complexity and a polynomial reduction in the gate complexity over naïve algorithms for the task of unitary (mixed) Schur sampling. Further, we show that if the input state has limited rank, the gate and memory complexities of our streaming algorithm as well as the algorithms for the full Schur and mixed Schur transforms are further reduced. Our work generalizes and improves on the results in arXiv2309.11947. Copyright © 2024, The Authors. All rights reserved.

关键词： consensus algorithm

Secure and Scalable IoT Networks: Optimizing Blockchain and SDN for Smart Environments

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Secure and Scalable IoT Networks: Optimizing Blockchain and ...

Blockchain Technology and Information Security (ICBCTIS), International Conference on

作者： Arpit Jain Dignesh Kumar Khatri Aravind Ayyagiri Chandrasekhara Mokkapati Vijay Bhasker Reddy Bhimanapati Laith H. Alzubaidi Department of Computer Science & Engineering Koneru Lakshmaiah Education Foundation Andhra Pradesh India Department of Computer Science & Engineering Gujarat University Gujarat India Department of Computer Science & Engineering Wichita State University Dublin C.A. USA Department of CS & IT Jawaharlal Nehru Technological University Hyderabad India Department of Computer Science Southern University and A&M College L.A. U.S.A. The Islamic university Najaf Iraq Najaf Iraq

ISBN: (数字)9798331528324

ISBN: (纸本)9798331528331

As a result of the Internet of Things, high-speed data transmission and ultra-low latency are achieved in various applications. Data tampering in IoT networks can be caused by malicious or accidental interference, however. By combining blockchain technology with software-defined networking (SDN), we can mitigate these problems. IoT devices and SDN controllers will be able to communicate peer-to-peer by using public and private blockchains. For devices with limited resources, it is an ideal solution since it eliminates Proof-of-Work (PoW) and incorporates distributed trust. In this paper, we present a new Proof-of-Authority (PoA) consensus algorithm that is designed to improve the consistency and reliability of edge devices within the IoT ecosystem, as well as to ensure a high level of trust across IoT ecosystems. During experiments, the integration of SDN and blockchain outperformed existing models in terms of throughput, delay, response time, and CPU utilization, including Blockchain Fundamentals (BCF), AS Cooperative Interdomain Reputation (ASCIR), and Blockchain-based SDN-enabled Secure Routing (BSDNSR).

关键词： Biological system modeling Ecosystems consensus algorithm Throughput Blockchains Peer-to-peer computing Delays Internet of Things Time factors Software defined networking

An Evaluation of Massively Parallel algorithms for DFA Minimization

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arXiv 2024年

作者： Martens, Jan Wijs, Anton Leiden University Netherlands Eindhoven University of Technology Netherlands

We study parallel algorithms for the minimization of Deterministic Finite Automata (DFAs). In particular, we implement four different massively parallel algorithms for DFA minimization on Graphics Processing Units (GPUs). Our results confirm the expectations that the algorithm with the theoretically best time complexity is not practically suitable to run on GPUs due to the large amount of resources needed. We empirically verify that parallel partition refinement algorithms from the literature perform better in practice, even though their time complexity is worse. Lastly, we introduce a novel algorithm based on partition refinement with an extra parallel partial transitive closure step and show that on specific benchmarks it has better run-time complexity and performs better in practice. © 2024, CC BY.

关键词： consensus algorithm

PARALLEL GRAPH DRAWING algorithm FOR BIPARTITE PLANAR GRAPHS

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arXiv 2024年

作者： Jain, Naman The International School Bangalore Bangalore India

We give a parallel O(log(n))-time algorithm on a CRCW PRAM to assign vertical and horizontal segments to the vertices of any planar bipartite graph G in the following manner: i) Two segments cannot share an interior point ii) Two segments intersect if and only if the corresponding vertices are adjacent, which uses a polynomial number of processors. In other words, represent vertices of a planar bipartite graph as parallel segments, and edges as intersection points between these segments. Note that two segments are not allowed to cross. Our method is based on a parallel algorithm for st-numbering which uses an ear decomposition search. © 2024, CC BY.

关键词： consensus algorithm

Fairness and Efficiency in Online Class Matching

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arXiv 2024年

作者： Hajiaghayi, MohammadTaghi Jahan, Shayan Chashm Sharifi, Mohammad Shin, Suho Springer, Max University of Maryland College Park United States Sharif University of Technology Tehran Iran

The online bipartite matching problem, extensively studied in the literature, deals with the allocation of online arriving vertices (items) to a predetermined set of offline vertices (agents). However, little attention has been given to the concept of class fairness, where agents are categorized into different classes, and the matching algorithm must ensure equitable distribution across these classes. We here focus on randomized algorithms for the fair matching of indivisible items, subject to various definitions of fairness. Our main contribution is the first (randomized) non-wasteful algorithm that simultaneously achieves a 1/2 approximation to class envy-freeness (CEF) while simultaneously ensuring an equivalent approximation to the class proportionality (CPROP) and utilitarian social welfare (USW) objectives. We supplement this result by demonstrating that no non-wasteful algorithm can achieve an α-CEF guarantee for α > 0.761. In a similar vein, we provide a novel input instance for deterministic divisible matching that demonstrates a nearly tight CEF approximation. Lastly, we define the "price of fairness," which represents the trade-off between optimal and fair matching. We demonstrate that increasing the level of fairness in the approximation of the solution leads to a decrease in the objective of maximizing USW, following an inverse proportionality relationship. © 2024, CC BY.

关键词： consensus algorithm

Persistent (Co)Homology in Matrix Multiplication Time

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arXiv 2024年

作者： Morozov, Dmitriy Skraba, Primoz Lawrence Berkeley National Laboratory United States School of Mathematical Sciences Queen Mary University of London United Kingdom

Most algorithms for computing persistent homology do so by tracking cycles that represent homology classes. There are many choices of such cycles, and specific choices have found different uses in applications. Although it is known that persistence diagrams can be computed in matrix multiplication time for the more general case of zigzag persistent homology [1], it is not clear how to extract cycle representatives, especially if specific representatives are desired. In this paper, we provide the same matrix multiplication bound for computing representatives for the two choices common in applications in the case of ordinary persistent (co)homology. We first provide a fast version of the reduction algorithm, which is simpler than the algorithm in [1], but returns a different set of representatives than the standard algorithm [2]. We then give a fast version of a variant called the row algorithm [3], which returns the same representatives as the standard algorithm. © 2024, CC BY.

关键词： consensus algorithm